Results 1 to 4 of 4

Math Help - Statement about the product AB of two square matrices, true or false?

  1. #1
    Member
    Joined
    Feb 2011
    Posts
    75

    Statement about the product AB of two square matrices, true or false?

    Is this statement true or false

    if false a counterexample is needed

    if true then an explanation

    The product
    AB of two square matrices can only have an inverse if A and B

    both have inverses.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    What ideas have you had so far?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    A matrix specifies a linear transformation. If a matrix is (or is not) invertible, what does that tell you about the rank of the associated linear transformation? Multiplying the matrices corresponds to composing the transformations.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,232
    Thanks
    1795
    Another way of thinking about it- a matrix is invertible if and only if its determinant is non-zero. And det(AB)= det(A)det(B).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: February 21st 2011, 05:37 AM
  2. Limit statement; True or False
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 14th 2010, 10:32 PM
  3. Is this statement true or false?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 24th 2010, 12:55 AM
  4. True or False Statement?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 11th 2009, 09:04 AM
  5. Surjections and a true/false statement.
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: December 17th 2008, 05:43 AM

Search Tags


/mathhelpforum @mathhelpforum